SOLUTION: Can you show me how to solve x^3-6x^2-9x=0?

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Question 709881: Can you show me how to solve x^3-6x^2-9x=0?
Answer by josh_jordan(263) About Me  (Show Source):
You can put this solution on YOUR website!
To solve for x, first factor out an x from the left side of the equal sign. This gives us

x%28x%5E2+-+6x+-+9%29+=+0

We know know that 0 is one of the values of x.

To find the other two values, use the quadratic formula on the quadratic equation inside the parentheis: x%5E2+-+6x+-+9

x=%28-%28-6%29%2B-sqrt%28-6%5E2-4%2A1%2A%28-9%29%29%29%2F%282%2A1%29 =

x+=+%286%2B-sqrt%2836%2B36%29%29%2F2 =

x+=+%286%2B-sqrt%2872%29%29%2F2 =
x+=+%286%2B-6%2Asqrt%282%29%29%2F2

We can reduce this to lowest terms, by factoring out a 6 from the numerator:

x+=+%286%281%2B-sqrt%282%29%29%29%2F2, then dividing the factored 6, by two, giving us

x+=+3%281%2B-sqrt%282%29%29

Therefore, x = 0,3%2B3%2Asqrt%282%29%29,3-3%2Asqrt%282%29%29